Functional Chung laws for small increments of the empirical process and a lowerbound in the strong invariance principle
type: Item
instance of: scholarly article
title: Functional Chung laws for small increments of the empirical process and a lowerbound in the strong invariance principle
zbMATH Open document ID: 1240.60102
author: Ph. Berthet
published in: Periodica Mathematica Hungarica
publication date: 2011-12-19T00:00:00Z
review text: Consider the set \(\Theta_{n}\) of all \(\alpha_{n}\)-sized increment processes of the uniform empirical process \(\alpha_{n}\) on \([0,1]\). The author computes the exact rate of clustering of \(\Theta_{n}\) to any Strassen function having Lebesgue derivative of bounded variation.
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 5990587
zbMATH Keywords: Chung and Strassen functional laws
zbMATH Keywords: empirical and Poisson processes
zbMATH Keywords: Brownian bridge
zbMATH Keywords: increment processes
zbMATH Keywords: small deviation probabilities
zbMATH Keywords: strong invariance principle
MaRDI profile type: Publication
full work available at URL: s10998-010-3067-2
OpenAlex ID: W2070217421
cites work: Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm
cites work: On the rate of clustering to the Strassen set for increments of the uniform empirical process
cites work: Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes
cites work: Some exact rates in the functional law of the iterated logarithm
cites work: Hungarian constructions from the nonasymptotic viewpoint
cites work: On the Maximum Partial Sums of Sequences of Independent Random Variables
cites work: A relation between Chung's and Strassen's laws of the iterated logarithm
cites work: A new method to prove strassen type laws of invariance principle. 1
cites work: How big are the increments of a Wiener process?
cites work: Q3326516
cites work: Q4035990
cites work: Functional laws of the iterated logarithm for small increments of empirical processes
cites work: Chung-type functional laws of the iterated logarithm for tail empirical processes
cites work: Functional laws of the iterated logarithm for the increments of empirical and quantile processes
cites work: Chung's law and the Csáki function
cites work: A lim inf result in Strassen's law of the iterated logarithm
cites work: An approximation of partial sums of independent RV'-s, and the sample DF. I
cites work: Lim inf results for Gaussian samples and Chung's functional LIL
cites work: A strong limit theorem for the oscillation modulus of the uniform empirical quantile process
cites work: Strong limit theorems for oscillation moduli of the uniform empirical process
cites work: A refinement of the KMT inequality for the uniform empirical process
cites work: A generalization of Strassen's functional law of iterated logarithm
cites work: Small ball probabilities for a centered Poisson process of high intensity
cites work: Q3395931
cites work: An invariance principle for the law of the iterated logarithm
cites work: The oscillation behavior of empirical processes
cites work: A law of the logarithm for kernel density estimators
DOI: 10.1007/S10998-010-3067-2
description: scientific article; zbMATH DE number 5990587